1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lapo4ka [179]
3 years ago
11

Let ????C be the positively oriented square with vertices (0,0)(0,0), (2,0)(2,0), (2,2)(2,2), (0,2)(0,2). Use Green's Theorem to

evaluate the line integral ∫????10y2x????x+4x2y????y∫C10y2xdx+4x2ydy.
Mathematics
1 answer:
bonufazy [111]3 years ago
3 0

Answer:

-48

Step-by-step explanation:

Lets call L(x,y) = 10y²x, M(x,y) = 4x²y. Green's Theorem stays that the line integral over C can be calculed by computing the double integral over the inner square  of Mx - Ly. In other words

\int\limits_C {L(x,y)} \, dx + M(x,y) \, dy =  \int\limits_0^2\int\limits_0^2 (M_x - L_y ) \, dx \, dy

Where Mx and Ly are the partial derivates of M and L with respect to the x variable and the y variable respectively. In other words, Mx is obtained from M by derivating over the variable x treating y as constant, and Ly is obtaining derivating L over y by treateing x as constant. Hence,

  • M(x,y) = 4x²y
  • Mx(x,y) = 8xy
  • L(x,y) = 10y²x
  • Ly(x,y) = 20xy
  • Mx - Ly = -12xy

Therefore, the line integral can be computed as follows

\int\limits_C {10y^2x} \, dx + {4x^2y} \,dy = \int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy

Using the linearity of the integral and Barrow's Theorem we have

\int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy = -12 \int\limits_0^2\int\limits_0^2 xy \, dx \, dy = -12 \int\limits_0^2\frac{x^2y}{2} |_{x = 0}^{x=2} \, dy = -12 \int\limits_0^22y \, dy \\= -24 ( \frac{y^2}{2} |_0^2) = -24*2 = -48

As a result, the value of the double integral is -48-

You might be interested in
1. A system of linear equations that has one solution has slopes that are__________
algol13

Answer:

different

Step-by-step explanation:

different slopes gives one solution

same slopes with different constant has no solution

same slopes and constants has many solutions

3 0
3 years ago
Is this right?? please help!
Ganezh [65]

Answer:

  6 < x < 8

Step-by-step explanation:

The compound inequality in this instance represent the "and" condition, not the "or" condition.* We might solve it like this.

  -47 > 1 -8x > -63 . . . . given

Multiply by -1:

  47 < -1 +8x < 63

Add 1:

  48 < 8x < 64

Divide by 8:

  6 < x < 8

______

* You can tell this is the case by looking at the ends of the given statement:

  -47 > -63 . . . . a true statement, so the solution set will be an intersection, not a union.

4 0
3 years ago
A race
sashaice [31]

Answer: 187.7 mph

Step-by-step explanation:

v = 125 mph

t = 1.2 min

v2 = ?

t2 = 0.8 min

We can use the rule of 3 here. It's the inverse rule of 3 because as time decreases, speed increases.

\frac{125mph}{x} =\frac{1.2min}{0.8min}

x = \frac{(125)(1.2)}{0.8}

x=187.5mph

7 0
3 years ago
The cost of a hotel room for 5 nights is $610. there is a 9.5% tax
vlabodo [156]

Answer:

wrong it is 667.95

Step-by-step explanation:

8 0
2 years ago
For some integer n, the first, the third and the fifth terms of an arithmetic sequence are respectively 3n, 5n – 6, and 11n + 8.
Mazyrski [523]

Answer:

a₄=8n+1= -39.

Step-by-step explanation:

1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then

2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.

3) if n=-5, then the 4th term is:

a_4=\frac{a_5+a_3}{2}; \ = > \ a_4=\frac{11n+8+5n-6}{2}=8n+1;

or a₄=-39.

8 0
2 years ago
Other questions:
  • For what values of x will the result of 5x be greater than 1
    7·1 answer
  • What is the answer to a0/12 = -6
    8·1 answer
  • Algebra 2 help please
    6·1 answer
  • Use the quadratic equation x^2+3x+5=0 to answer the questions. A: What is the discriminant of the quadratic equation? B: Based o
    8·2 answers
  • What is the eighth multiple of 12​
    15·2 answers
  • Find the area of the following<br> rhombus:<br> 6 cm<br> 10 cm<br> 8 cm<br> A=121 cm2
    13·2 answers
  • Solve for e <br> Give an exact answer <br> 0.75(8 + e) = 2 - 1.25e
    15·1 answer
  • List the first 4 terms of the sequence 3n² + 1​
    15·2 answers
  • Help me! I'll give brainliest.
    7·2 answers
  • Choose the function that correctly identifies the transformation of f(x) = x2 shifted four units right and seven units down.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!